Combinatorial Type Problems for Triangulation Graphs
The main result in this thesis bounds the combinatorial modulus of a ring in a triangulation graph in terms of the modulus of a related ring. The bounds depend only on how the rings are related and not on the rings themselves. This may be used to solve the combinatorial type problem in a variety of...
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| Format: | Others |
| Language: | English English |
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Florida State University
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| Online Access: | http://purl.flvc.org/fsu/fd/FSU_migr_etd-0794 |
| Summary: | The main result in this thesis bounds the combinatorial modulus of a ring in a triangulation graph in terms of the modulus of a related ring. The bounds depend only on how the rings are related and not on the rings themselves. This may be used to solve the combinatorial type problem in a variety of situation, most significant in graphs with unbounded degree. Other results regarding the type problem are presented along with several examples illustrating the limits of the results. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of
the requirements for the degree of Doctor of Philosophy. === Degree Awarded: Summer Semester, 2006. === Date of Defense: July 6, 2006. === Graph Theory, Circle Packing, Discrete Conformal Geometry, Conformal Type === Includes bibliographical references. === Philip Bowers, Professor Directing Dissertation; Lois Hawkes, Outside Committee Member; Steve Bellenot, Committee Member; Eric Klassen, Committee Member; Craig Nolder, Committee Member; Jack Quine, Committee Member. |
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